Finite element analysis (FEA) is a computer implemented method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modem digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
FEA is becoming increasingly popular with automobile manufacturers for optimizing both the aerodynamic performance and structural integrity of vehicles. Similarly, aircraft manufacturers rely upon FEA to predict airplane performance long before the first prototype is ever developed. One of the popular FEA tasks is to simulate an impact event such as car crash. A problem associated with crashworthiness simulation is to properly simulate spot welds used for connecting two parts (e.g., sheet metal) in a structure.
Spot welding is a type of resistance welding used to weld various sheet metal products. Typically the sheets are in the 0.5-3.0 mm thickness range. The process uses two shaped copper alloy electrodes to concentrate welding current into a small “spot” and to simultaneously clamp the sheets together. One of the most common applications of spot welding is in the automobile manufacturing industry, where it is used almost universally to weld the sheet metal to form a car.
In a typical car, there are about 4,000-8,000 spot welds connecting 300-600 body parts to form the vehicle structure. For accurate simulation of the vehicle as a whole, those spot welds have to be modeled accurately. Spot welds are typically placed 2-3 centimeters apart, and each spot weld has a diameter between 4 to 9 millimeters (mm). Traditionally, each of the spot welds has been modeled with a very short beam element (e.g., length of 1-2 millimeters) in FEA. For example, in the 1990s, spot welds were modeled using two-node rigid bodies with the requirement that the nodal locations of the spot weld parts be at the physical location of the spot weld. This prior art approach required much work in creating the FEA model due to the effort to properly locate nodal points precisely at the weld locations. As the modern computer improves, the finite element models representing a vehicle have become huge (e.g., more than 4,000,000 elements varying in size from 2-4 mm). Thereby, the size of elements around the spot welds becomes smaller than the spot weld diameter. Representing spot welds using beam elements are not adequate any more, instead solid elements are used. In certain cases, spot welds have been modeled with more than one solid element. Furthermore, in a car crashworthiness simulation, spot weld failure needs to be considered and determined. The spot weld failure determination method for beam element has been well established. However, this method is inconsistent with traditional material failure method used in solid elements.
Therefore, it would be desirable to have an improved method for determining spot weld failure in a finite element analysis regardless which type of element is used for representing spot welds.